Relative Surprise Confidence Intervals

[ParadaCarleton]

May implement this myself if I have more time -- relative surprise confidence intervals are a set of credible intervals that can be shown to have several very appealing properties:

1. Transformation invariance.
2. Minimize the prior probability that the interval covers an incorrect value.
3. Coverage very close to their nominal coverage -- there is a 95% chance that the true parameter value lies within the traditional credible interval, but will not cover the true value 95% of the time (except asymptotically). Confidence intervals have the opposite set of properties. While statisticians mostly understand the difference between these, laypeople do not. Relative surprise confidence intervals maximize the coverage frequency among all possible credible intervals. As a result, they minimize the harm caused by assuming a credible interval satisfies the confidence interval property.